3=3e+2/4e+7

Solution for 3=3e+2/4e+7 equation:

3=3e+2/4e+7

We move all terms to the left:

3-(3e+2/4e+7)=0


Domain of the equation: 4e+7)!=0

e∈R


We get rid of parentheses

-3e-2/4e-7+3=0

We multiply all the terms by the denominator


-3e*4e-7*4e+3*4e-2=0

Wy multiply elements

-12e^2-28e+12e-2=0

We add all the numbers together, and all the variables

-12e^2-16e-2=0

a = -12; b = -16; c = -2;
Δ = b2-4ac
Δ = -162-4·(-12)·(-2)
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{10}}{2*-12}=\frac{16-4\sqrt{10}}{-24}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{10}}{2*-12}=\frac{16+4\sqrt{10}}{-24}
$